The present disclosure relates to a diagonal generating method in which an axial feed of the tool having a diagonal ratio given by the ratio between the axial feed of the tool and the axial feed of the workpiece takes place during the machining. In this respect, the term “axial feed of the tool” means a relative movement of the tool to the workpiece in the axial direction of the tool. The term “axial feed of the workpiece” means a relative movement of the tool to the workpiece in the axial direction of the workpiece. Depending on the embodiment of the gear manufacturing machining machine on which the method in accordance with the present disclosure is carried out, different machine axes can be used for the production of the axial feed of the tool and the axial feed of the workpiece. Only the tool can, for example, be moved both in the direction of its axis and in the direction of the axis of the workpiece. Since it is a generating process, the rotational movements of the tool and of the workpiece are furthermore coupled. The workpiece can in particular be a gear.
Different regions of the tool successively come into contact with the workpiece during the gear manufacturing machining in the diagonal generating method due to the axial feed of the tool, which is also called shifting. Such diagonal generating methods are typically used to achieve a wear of the tool surface which is as uniform as possible.
A diagonal generating method is known from EP 1 995 010 B1 in which a tool having a gear tooth geometry corrected for crowning is used to produce a crown-modified workpiece. For this purpose, the delivery of the tool to the workpiece is likewise changed in a crowning manner during the machining process. In this respect, the diagonal ratio, which is defined as the ratio of the paths covered during the machining in the axial direction of the tool and in the axial direction of the workpiece, is set such that a desired twist is produced.
A method is furthermore known from DE 10 2012 015 846 A1 in which, in the diagonal generating method, a tool is used which is modified in its surface geometry, wherein the surface geometry has a constant value in the generating pattern at least locally in a first direction of the tool and is given by a function f(x) in a second direction which extends perpendicular to the first direction. This modification of the tool leads to a corresponding modification of the surface geometry of the workpiece. In this respect, the diagonal ratio used for the machining is inter alia selected such that the modification of the tool produces the desired modification of the workpiece.
It is the object of the present disclosure to further develop and to improve the diagonal generating method known from the prior art. A possible objective of the present disclosure can be to improve the flexibility of the machining process, in particular with respect to the modifications which can be produced. Another objective of the present disclosure can be to be able to better use the available grinding regions of the grinding tools.
This object is achieved in accordance with the present disclosure by the independent claims of the present application. Advantageous embodiments of the present disclosure form the subject of the dependent claims.
The present disclosure shows a method for the gear manufacturing machining of a workpiece by a diagonal generating method with which the workpiece is gear tooth machined by the rolling off of a tool. During the machining of the workpiece, an axial feed of the tool with a diagonal ratio given by the ratio between the axial feed of the tool and the axial feed of the workpiece takes place. In accordance with the present disclosure, the diagonal ratio is varied as part of the machining of a workpiece. The method in accordance with the present disclosure for the gear tooth machining can be a method for hard fine machining and/or a grinding method. The workpiece may be a gear wheel. A grinding worm is optionally used as the tool.
The method in accordance with the present disclosure can in particular be used for the machining of cylindrical or conical workpieces or gear teeth. The gear teeth can be symmetrical or asymmetrical.
It was admittedly known in the diagonal generating methods known from the prior art to select a specific diagonal ratio with which the gear manufacturing machining can then take place before the carrying out of the method. However, work was carried out with a constant diagonal ratio during the machining of the workpiece itself. The inventor of the present disclosure has now recognized that a variety of new possibilities are opened up by a variation of the diagonal ratio as part of the machining of a workpiece.
The variation of the diagonal ratio in accordance with the present disclosure may take place within the framework of a method for the manufacture of a workpiece having a corrected gear tooth geometry and/or a modified surface structure in which a corresponding modification is produced on the surface of the workpiece by means of a specific modification of the surface geometry of the tool and by means of a mapping of the surface of the tool produced by the diagonal generating method and depending on the diagonal ratio onto the surface of the workpiece. The diagonal ratio can in particular be varied as part of such a process to provide additional variation possibilities in the production of the modifications.
As part of such a method for the production of a modified surface geometry of the workpiece, the specific modification of the surface geometry of the tool can be produced in that the position of the dresser to the tool during the dressing is varied in dependence on the angle of rotation of the tool and/or on the tool width position. A particularly simple possibility of producing modifications of the surface geometry of the tool hereby results.
The dressing can take place on one flank or on two flanks. The dressing can furthermore take place in one stroke or in a plurality of strokes.
The profile roller dresser can in particular be in contact with the tooth of the tool from the root region to the tip region during dressing so that the modification takes place in one stroke over the total tooth depth.
The profile roller dresser can alternatively only be in contact with the tooth of the tool in part regions between the base and the tip during the dressing so that the modification takes place in a plurality of strokes over the tooth depth.
The dressing of the tooth tip can take place via a tip dressing tool.
The present disclosure can in principle also be used with non-dressable tools. In this case, the modifications of the tool are already produced during the manufacture of the tools and cannot be changed during the machining process of a workpiece.
In case of a non-dressable grinding tool, the inventive modification of the surface geometry can be produced during the manufacturing process in exactly the same way as described in the following for dressable tools, with the only change that instead of a dressing tool, a corresponding manufacturing tool is used, for example a rolling die.
In case that the tool is a hobbing cutter, it has to be manufactured in such a way that the enveloping body of the hobbing cutter has the modification provided by the present disclosure. With respect to a hobbing cutter, the term “modification of the surface geometry of the tool” as used in the context of the present disclosure is to be understood as a modification of the surface geometry of the enveloping body of the hobbing cutter.
The present disclosure may however be used with a dressable tool. In particular, the modification of the surface geometry of the tool may be generated during a dressing step.
The modification of the surface geometry of the workpiece on the tooth flank may have a constant value in the generating pattern in at least a first region and/or locally in a first direction of the workpiece, whereas the modification is given by a function FFt2 in a second direction of the workpiece which extends perpendicular to the first direction.
Provision can furthermore be made that the modification of the surface geometry of the tool used for producing the modification of the surface geometry of the workpiece can furthermore have a constant value in the generating pattern at least in a first region and/or locally in a first direction of the tool and is further optionally given by a function FFt1 in a second direction of the tool which extends perpendicular to the first direction. The function FFt1 on the tool may be the same function, optionally compressed linearly by a factor, as the function FFt2 on the workpiece. The linear compression can relate to the argument of the function and/or to the magnitude of the function. The modification on the workpiece naturally has the opposite sign to the modification on the tool since elevated portions on the tool surface produce recesses on the workpiece surface and vice versa. In the normal section, in particular FFt1(x)=−FFt2 (cx) can apply in this respect, i.e. there is only compression with respect to the argument; an additional constant factor k can in contrast be present in the transverse section with respect to the magnitude of the function, i.e. FFt1(x)=−k*FFt2 (cx). The factors k and c can be larger than or less than 1 depending on the specific conditions.
In accordance with the present disclosure, in this respect, the macrogeometry of the tool and/or the line of action of the dressing tool and/or the diagonal ratio and/or the compression factor can be selected such that the modification of the tool along a first line on which the contact point moves on the tool in the machining of the workpiece corresponds to the desired modification of the workpiece along a second line on which the contact point moves on the workpiece. The parameters are in particular selected such that the modification desired on the workpiece is produced by the modification produced on the tool.
The variation of the diagonal ratio in accordance with the present disclosure can, however, not only be used in such processes for the manufacture of a workpiece having a corrected gear tooth geometry, but also in a diagonal generating method in which non-modified tools are used and/or in which the workpieces are not modified.
In accordance with the present disclosure, involute gear teeth may be produced. The modifications specified in accordance with the present disclosure relate to a modification with respect to a surface geometry given by involute gear teeth. In this respect, involute tools are advantageously used which are optionally correspondingly modified.
In accordance with a first variant of the present disclosure, work can be carried out with different diagonal ratios for the machining of different regions of the workpiece. The diagonal ratio can in particular be varied in such a process, while the workpiece is in contact with the tool and is gear tooth machined by the tool, i.e. during an ongoing machining step. Alternatively or additionally, the diagonal ratios used for the feed of the tool during the carrying out of a machining step differ at at least two points of the axial feed of the tool and/or workpiece covered during the machining. In this respect, the diagonal ratio can in particular be varied, while the width of the gear teeth is moved over as part of a machining step.
In a second variant, which is combined with the first variant in a possible embodiment, work can be carried out with different diagonal ratios on the use of different regions of the tool.
On the one hand, on the use of different regions of the tool which, however, belong to a contiguous machining region used during a machining step for the machining of the workpiece, work can be carried out with different diagonal ratios. Such a procedure is produced automatically due to the diagonal feed grinding process in accordance with the present disclosure in which different regions of the workpiece are machined with different regions of the tool during a machining step when, in accordance with the first variant, work is carried out with different diagonal ratios for the machining of different regions of the workpiece.
However, even when the tool has two separate regions used for different machining steps, work can also be carried out with different diagonal ratios in these different regions. In this case, the two different regions of the tool can be used to machine the same region of the workpiece.
In both variants of the present disclosure, work can be carried out with a constant diagonal ratio within the respective regions in a possible embodiment of the present disclosure. In this respect, two or more regions can in particular be provided within which work is respectively carried out using a constant diagonal ratio, with the diagonal ratios of at least two regions differing.
Alternatively to this, the diagonal ratio can be varied during the machining of the workpiece in dependence on the axial feed of the tool. In this respect, the diagonal ratio can be given as a non-constant and optionally stead function of the axial feed in at least in a region of the axial feed. The diagonal ratio can in particular be freely predefined in dependence on the axial feed.
As already presented above, the variation of the diagonal ratio in accordance with the present disclosure can be used to influence the modifications resulting in accordance with the present disclosure in the above-described method for the production of modified surfaces of a workpiece. In this respect, the change of the diagonal ratio can in particular be used to vary the orientation of the modifications resulting on the workpiece.
In this respect, in the modified diagonal generating method, the modified surface of the tool is mapped onto the surface of the workpiece, with this mapping depending on the selected diagonal ratio. The first direction of the workpiece onto which the first direction of the tool is mapped in which the modification is constant is in particular dependent on the selected diagonal ratio. A different orientation of the modification in different regions of the workpiece can thus be achieved by the variation of the diagonal ratio during the machining of these different regions of the workpiece.
If work is carried out in two or more regions in each case with a constant, but different diagonal ratio, different orientations of the modifications accordingly result, but which are constant within the regions. If, in contrast, the diagonal ratio is varied within a region, a corresponding variation in the orientation results. If the diagonal ratio is given by a steady, non-constant function, a steady variation in the orientation of the modification accordingly results.
In a possible embodiment of the present disclosure, the extent of at least one line of constant modification can be predefined and the variation of the diagonal ratio in dependence on the axial feed and in particular the non-constant function by which this is given can be determined from this. A line of constant modification which does not form a straight line in the generating diagram in particular results in a non-constant function in this respect. The extent of at least one line of constant modification may be freely predefined at least within certain conditions.
In this respect, the function which describes the diagonal ratio in dependence on the axial feed can have at least one region in which it has a steady non-constant extent. This would correspond to a steady curvature of the line of constant modification.
The variation of the diagonal ratio on the sweeping over of a modified region of the workpiece may take place such that the orientation of the modification varies in this region.
The variation of the diagonal ratio in accordance with the present disclosure can be used both on the use of a cylindrical tool and on the use of a conical tool. In this respect, the modification of the workpiece can be influenced in both cases by the variation of the diagonal ratio.
A conical cool, i.e. a tool having a conical basic shape, may be used for the carrying out of a method in accordance with the present disclosure in which a variation of the diagonal ratio takes place while the tool is guided along the workpiece in the width direction. The modifications resulting from the variation of the diagonal ratio can hereby additionally be specifically influenced by the setting of certain parameters of the tool or of the machining process. In this respect, a conical tool is may be used when the diagonal ratio is given as a steady, non-constant function.
The tool in accordance with the present disclosure having a conical basic shape may have involute gear teeth which can, however, optionally have modifications. Involute gear teeth have a geometry which is produced by the generating machining step between a cylinder and a rack. The conical basic shape is produced in that the axis of rotation of the cylinder is tilted toward the main plane of the rack in the course of this generating machining step.
In accordance with a preferred embodiment, the cone angle of the tool is greater than 1′, further optionally greater than 30′, and further optionally greater than 1°. The cone angle of the tool is, however, optionally less than 50°, optionally less than 20°, and further optionally less than 10°.
The modifications which can be achieved by the variation of the diagonal ratio can in particular be specifically influenced on the use of a conical tool by a suitable choice of at least one, and optionally a plurality of parameters of the machining process and/or of the macrogeometry of the tool, in particular of the axial cross angle and/or of the axial spacing and/or of the cone angle and/or of the profile angle of the tool.
On the one hand, a desired orientation of the modification on the left and right tooth flanks can hereby be achieved. The present method in particular comprises a step of predefining a desired alignment of the modification on the left and right tooth flanks and of determining a parameter suitable herefor and/or of a combination of parameters of the machining process and/or of the macrogeometry of the tool suitable herefor.
The modification on a tooth flank as such can furthermore also be influenced by the suitable choice of at least one, and optionally of a plurality of parameters of the machining process and/or of the macrogeometry of the tool. In this respect, the orientation and/or pitch of the modification can in particular be influenced in different regions of the tooth flank.
The same possibilities also result when the workpiece has conical gear teeth, and indeed on the use of both a conical and of a cylindrical tool.
The tool in accordance with the present disclosure can have at least one modified region and one non-modified region in a first variant. In this respect, the tool optionally has two modified regions between which a non-modified region lies. If two modified regions are provided, the orientation of the modifications and in particular the first direction of the modifications can be identical in these regions. A particularly simple dressing behavior hereby results. Work is then optionally carried out with different diagonal ratios in the two modified regions in order hereby to achieve a different orientation of the modification on the workpiece.
In a second variant, the tool can have two regions having different modifications. The modifications can in particular have different orientations, in particular different first directions. Even greater degrees of freedom hereby result in the production of differently oriented modifications on the workpiece.
The second variant can furthermore also be combined with the first variant in that, in addition to the two regions having different modifications, a non-modified region is provided which can in particular be arranged between the two modified regions.
If a plurality of modified regions are provided, the modifications in the two regions can differ with respect to the form FFt of the modification in the second direction.
Tools modified in accordance with the present disclosure can in particular be used to carry out different modifications on different regions of the workpiece, for example to produce different reliefs, and in particular differently oriented reliefs, at the upper edge and lower edge.
In an alternative embodiment of the present disclosure, the tool can have at least two regions which are used successively for the machining of the same region of the workpiece. The two regions can in particular be a rough machining region and a fine machining region. The rough machining region is used to achieve a greater material removal with a smaller precision. The fine machining region is, in contrast, used after the rough machining to improve the quality of the surface geometry.
In this respect, the machining steps with the different regions are advantageously carried out with different diagonal ratios. Work can in particular be carried out with a different diagonal ratio in the rough machining step than in the fine machining step. The diagonal ratios during the respective machining steps can in contrast be kept constant.
The use of different diagonal ratios in the two tool regions allows the given tool width to be used better. In this respect, in particular one of the two regions can be shorter than the other region although they are used for machining the same workpiece. Accordingly, only the diagonal ratio has to be adapted to the respective width of the machining region of the tool.
The regions used for machining the workpiece may use the total tool width.
Such a procedure is of advantage independent of whether work is carried out with a modified tool or not.
In a preferred embodiment of the present disclosure, however, the fine machining region is in particular modified. Depending on the size of the modification, the rough machining region, in contrast, does not necessarily have to be modified. It can, however, likewise be modified.
If both regions, and in particular both the rough machining region and the fine machining region are modified in this respect, the modifications each have a different orientation in a possible embodiment. In this respect, the modification which is to be produced on the workpiece by the two regions is naturally the same in each case. However identical modifications in the two regions would be mapped differently onto the workpiece due to the respective different diagonal ratios. The modifications are therefore optionally differently oriented in the two regions so that they are each mapped on the same direction on the workpiece while taking account of the different diagonal ratio. In this respect, a non-dressable tool can in particular be used since there is greater freedom in the manufacture of the modifications on such a tool. With dressable tools, in contrast, there may be a restriction due to the contact line of the dresser.
In an alternative embodiment, both regions, and in particular both the rough machining region and the fine machining regions can be modified and have an identical orientation of the modifications. Such tools can be manufactured more easily by the above-described dressing process since the line of action of the dresser into the tool and thus the direction of the modification on the tool can hardly be changed. This admittedly results in a different orientation of the modification on the tool due to the different diagonal ratios in the two regions. Since, however, the rough machining region is anyway only used for a coarse machining and the final surface shape is only produced by the fine machining step, this can be accepted in some cases.
In this case, the modification of the rough machining region only approximately produces the desired modification on the gear teeth, with the actual modification, however, being in the permitted tolerance range. The diagonal ratio for the fine machining step is selected such that the desired orientation of the diagonal ratio results. The diagonal ratio for the rough machining step is, in contrast, may be selected such that the actual modification is in the permitted tolerance range. In this respect, the shape of the modifications, in particular the function FFt1, can be changed in the rough machining region over the fine machining region.
In accordance with the present disclosure, the modification can also generally only approximately produce the desired modification on the gear teeth in at least one region of the tool, in particular in the rough machining region, with the diagonal ratio used. The form of the modification and the diagonal ratio are advantageously selected such that the actual modification is in the permitted tolerance range.
In a further embodiment of the present disclosure, the tool can have at least two regions which are used successively for the machining of different regions of the workpiece. In accordance with the present disclosure, in this respect, the machining in the one region can take place with a different diagonal ratio than in the other region.
Such a procedure is also of advantage with unmodified tools, for example, if a specific region of the tool is subjected to greater load during the machining than another region. In this respect, work may be carried out with a larger diagonal ratio and thus a faster axial feed of the tool when the tool is loaded more and with a smaller diagonal ratio in regions in which the workpiece is loaded less. The greater load can in particular result in that more material has to be removed than in other regions. A more uniform wear of the tool over the tool width results by such a procedure so that dressing has to be carried out less. Alternatively or additionally, in regions in which smaller tolerances are permitted with respect to the geometry of the workpiece surface, work can be carried out with a larger diagonal ratio so that the tool wears less in this region.
In a further variant, the tool can, however, also have one modified region and one unmodified region, in which regions work is carried out with different diagonal ratios.
In this respect, the diagonal ratio in the unmodified region can be selected as smaller than in the modified region to reduce the width of the tool since the unmodified region can thus be used for machining a larger region of the workpiece and can be shorter than with a constant diagonal ratio. The larger diagonal ratio in the modified region can, in contrast, be determined by the desired orientation of the modification on the tooth flank or the desired resolution in the second direction. In another variant, the diagonal ratio in the unmodified region can be larger than in the modified region to reduce the load on the tool in this region. Such a procedure in particular makes sense when the unmodified region has to remove more material than the modified region.
In accordance with the present disclosure, it is possible to work in a region which is used for machining an upper or lower end region of the workpiece with a smaller diagonal ratio than in a region used for machining a middle region of the workpiece. For in the machining of the upper or lower end region of the workpiece, the total tool does not yet dip into the workpiece so that the loads are lower here.
In a further variant of the present disclosure, the tool can have two modified regions between which an unmodified region lies, with the regions being used consecutively for machining different regions of the workpiece. In this respect, work is may be carried out with different diagonal ratios in the two modified regions. Different modifications, and in particular modifications with different orientations and in particular with different first directions can in particular hereby be produced in the respective regions of the workpiece. The two modified regions of the tool can have the same orientation of the modification. Alternatively, however, different orientations of the modification can also be selected here. The two modified regions can in particular be regions for machining the lower or upper edges of the workpiece.
The modified region and the unmodified region may be arranged such that the extent of the contact point between the tool and the workpiece is completely in the unmodified region during the machining in at least one grinding position. It is hereby ensured that a position is available at which the diagonal ratio can be varied without hereby influencing the geometry of the gear teeth on the workpiece. This is achieved in that the diagonal ratio is varied in a grinding position in which the contact point between the tool and the workpiece only sweeps over the unmodified region of the tool so that there is no modification here which would be influenced by the diagonal ratio. In this respect, work can in each case be carried out with a constant diagonal ratio in both modified regions. In this case, the diagonal ratio may be kept constant for as long as the contact point between the tool and the workpiece extends through one of the modified regions.
It is, however, conceivable in addition to such a procedure to vary the diagonal ratio steadily, for example in a transition region between a modified region and an unmodified region. The first directions in which the modification is constant, however, hereby no longer extend in parallel with one another in this transition region.
In addition to the method in accordance with the present disclosure, the present disclosure furthermore comprises a tool for the carrying out of a method such as was described above. The tool can in particular have at least two regions which can be used successively for the machining of the same region of the workpiece, with the two regions having a different width. In this respect, the width of the two regions is adapted to the respective diagonal ratio. The two regions can in particular be a rough machining region and a fine machining region.
The at least two regions may take up the total width of the tool.
Alternatively or additionally, the tool can have at least one modified region and one unmodified region which can be used successively for the machining of different regions of the workpiece. Alternatively or additionally, the tool can have two modified regions between which an unmodified region lies and which can be used successively for the machining of different regions of the workpiece. In a possible embodiment of the present disclosure, the two modified regions of the tool can be modified differently and can in particular have modifications with different orientations. The tool in accordance with the present disclosure is may be configured as was already shown in more detail above.
The tool can have a conical basic shape in a possible embodiment. In accordance with a preferred embodiment, the cone angle of the tool is greater than 1′, further optionally greater than 30′, and further optionally greater than 1°. The cone angle of the tool is, however, optionally less than 50°, optionally less than 20°, and further optionally less than 10°.
The present disclosure furthermore comprises a method for the dressing of a tool for the provision of a tool such as was described above or such as can be used in a method in accordance with the present disclosure for the machining of a workpiece. In this respect, in accordance with the present disclosure, the desired modification of the tool is produced by a variation of the machine kinematics during the dressing process. In this respect, the position of the dresser relative to the tool can in particular be varied in dependence on the angle of rotation of the tool and/or on the tool width position.
In this respect, the tool can have a modification with the same orientation over its total active surface. At least one modified region and at least one unmodified region and/or at least two regions having different modifications are, however, optionally produced. A modified tool such as was already described above is further optionally produced in this respect.
The present disclosure furthermore comprises a gear manufacturing machine for carrying out a machining method in accordance with the present disclosure and/or for carrying out a dressing method in accordance with the present disclosure such as was described in more detail above. The gear manufacturing machine advantageously has an input and/or calculation function via which different diagonal ratios and/or one variable diagonal ratio can be predefined and/or determined. The input function can in particular allow different diagonal ratios to be predefined in different regions and/or to predefine a diagonal ratio variable over the tool width. Alternatively or additionally, the input function can allow an input of a desired modification and determines the diagonal ratios required for producing such a modification. The gear manufacturing machine furthermore may have a control function which varies the diagonal ratio as part of the machining of a workpiece. The control function may vary the diagonal ratio in an automated manner.
The control function in accordance with the present disclosure can carry out at least two machining steps which take place successively and in which a respective other region of the tool is used for the machining of the same region of the workpiece. These steps can in particular be at least one rough machining step and at least one fine machining step.
In a possible embodiment of the present disclosure, the control takes place by the control function such that the machining steps take place using different diagonal ratios. The rough machining step and the fine machining step can in particular be carried out using different diagonal ratios. A non-dressable tool can in particular be used in this respect.
Alternatively or additionally, the control function can vary the diagonal ratio at least once in the course of a machining step. In this respect, the control function can in particular vary the diagonal ratio while the tools moves over the width of the gearing of the workpiece in a machining step. The control function may work with different diagonal ratios for the machining of different regions of the workpiece. In this respect, a functional variant can be provided which works with a constant diagonal ratio within the respective regions. In this case, an input function is may be provided which allows a definition of the regions and a predefinition of the respective diagonal ratios provided there. The control function can alternatively vary the diagonal ratio during the machining of the workpiece in dependence on the axial feed of the workpiece. The variation can in particular take place such that the diagonal ratio is given as a non-constant, optionally steady, function of the axial feed at least in a region of the axial feed. The gear manufacturing machine may have an input function which allows the predefinition of the non-constant function.
The gear manufacturing machine further may have a selection option by which two or more of the different input and/or control functions shown in more detail above can be selected.
The gear manufacturing machine in accordance with the present disclosure is further optionally a gear grinding machine. The gear grinding machine may have a tool spindle, a workpiece spindle and/or a spindle for the reception of a dresser, in particular of a dressing wheel, and machine axes for carrying out the relative movements required in accordance with the methods of the present disclosure between the workpiece and the tool and/or between the tool and the dresser in accordance with the present disclosure.
The present disclosure will now be explained in more detail with reference to embodiments and Figures.
The Figures only show w-z diagrams of cylindrical gear teeth by way of example. The w-z diagrams of conical gear teeth are generally not rectangular, are typically trapezoidal, since the evaluation region of the generating path varies over the gear tooth width.